IoT devices have been widely deployed in medical industry, in the objective of improving diagnostic accuracy and increasing the efficiency of healthcare systems. However, traditional centralized learning approaches often fall short in meeting strict privacy requirements and adapting to emerging diseases in clinical environment. To address this, we propose a novel federated continual learning (CL) framework for disease diagnosis (FCL4DD), designed to enable distributed and incremental learning of new disease classes while safeguarding data privacy. To combat catastrophic forgetting in CL, FCL4DD integrates a replay strategy powered by a weakly supervised diffusion model (WSDM) to generate historical data for diagnosis model training. The WSDM leverages weak supervision into diffusion model to capture the diverse characteristics of the real data, enabling the generation of high-quality synthetic samples that maintain the data's inherent variability. To overcome the challenges of nonindependent and identically distributed (non-IID) data in federated learning, WSDM is deployed at the central server to generate synthetic disease data that conforms to the global distribution. This synthetic data is then used to retrain client models, reducing discrepancies and enhancing performance consistency across clients. Evaluations on various datasets demonstrates that our method outperforms other state-of-the-art approaches, such as FedEWC, FedLwF, FedWeIT, TARGET, and DDDR, achieving up to a 4.85% accuracy improvement over the second-best method. Code are available at https://github.com/hysshy/FCL4DD.